Something's Wrong!? :grin: — Agent Smith

Your perspective.

:grin: Yep.

Your perspective. — jgill

What's wrong with it?

I've always had that Pythagorean feeling :snicker: that something's wrong! Irrational numbers?! WTF? :chin:

Hippasus of Metapontum (drowned at sea for mathematical heresy).

Yep. — Banno

What?

Examiners just want to test your understanding and methodology, but God wants to test your calculating skill as well.

If all the numbers in your calculations are such that they cancel out and leave you with a nice whole number answer, you're (almost) guaranteed to have solved the problem correctly. — Agent Smith

Assuming a more complex math problem, I think you would mean if the variables cancel out and you are left with an integer? Or maybe a rational number?

If you do mean whole numbers, the set of whole numbers is a countably infinite set, so just coming up with a single whole number doesn't guarantee a whole lot.

Why doesn't this rule apply to real life scenarios? Shouldn't we be going :chin: huh? when after trying to calculate some constants in math and science we find their values to be rather unwieldy/cumbersome/awkward like, for example, the numbers ππ and ee? — Agent Smith

What is unwieldy/cumbersome/awkward about $\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}.$? Just because there is no magical logic gate in your calculator than can represent $e$ as a ratio of two integers, or CAS that can compute it algebraically, doesn't mean there is something wrong there.

Should we also be amazed, puzzled and astonished that 1 is accurate to infinity? That 1 is the same as 1.000...?

Examiners just want to test your understanding and methodology, but God wants to test your calculating skill as well. — unenlightened

Good point! You understand teachers, math teachers to be precise, well!



To All

Consider the cancellations in a math calculation problem in an examination as a clue that you're on the right track, you've solved the problem correctly.

If you end up with a rational number that has a decimal extension, forget about irrational numbers, as an answer, alarm bells should go off in your head (you've either messed up with the calculations or are using the wrong method to solve the problem).

This is what I call the Pythagorean feeling (that something's wrong!).

Seems to me that both scenarios are real life scenarios. What use is math if not meant to be applied to real world scenarios? How is an impossible scenario described by math or language useful in real life?

Significant digits are the digits that are necessary in solving a real world problem. All other digits are unnecessary to the problem at hand. They may be useful for some other problem, but not the current one.

Depending on the number of humans and the fraction of them receiving an apple you could have ended up with an irrational number of humans. Can a human be divided and still be a human? So in the case of humans, we are only concerened about whole numbers and not any digits after the decimal.

We should keep in mind that math is a quantified representation of a world that is not composed of separate static objects but of intertwined relations. Math is more of a representaion of how the world is perceived than how the world is independent of perception, so we run into problems when we start to believe that the answers to math problems describe a world independent of our perceptions and goals.

@Harry Hindu

I have mixed feelings about irrational numbers. They've been proven to exist from the time of Pythagorss ($\sqrt 2$) but it's an open secret that the Pythagoreans were dead against it, it didn't make sense to them that such numbers exist.

"If all the numbers in your calculations are such that they cancel out and leave you with a nice whole number answer, you're (almost) guaranteed to have solved the problem correctly."

I would be curious to know what argument from mathematical philosophy supports this assertion? I can see a sense in which one could argue that set theory revolves around "nice whole numbers", but I am not sure how one might apply it to quantum mechanics or relativity theory.